quote:The law of superposition is an axiom that forms one of the bases of the sciences of geology, archaeology, and other fields dealing with geological stratigraphy. It is a form of relative dating. In its plainest form, it states that in undeformed stratigraphic sequences, the oldest strata will be at the bottom of the sequence. This is important to stratigraphic dating, which assumes that the law of superposition holds true and that an object cannot be older than the materials of which it is composed.
Instead of sedimentary layers, let's apply this law to the dense vein calcite formation found in Devil's Hole (Nevada), where the innermost layers had to be laid down first to form a base for later layers to deposit onto as they build up the dense vein calcite formation, so the deeper into the formation the older the calcite:
quote:Devils Hole is a tectonically formed cave developed in the discharge zone of a regional aquifer in south-central Nevada. (See Riggs, et al., 1994.) The walls of this subaqueous cavern are coated with dense vein calcite which provides an ideal material for precise uranium-series dating via thermal ionization mass spectrometry (TIMS). Devils Hole Core DH-11 is a 36-cm-long core of vein calcite from which we obtained an approximately 500,000-year-long continuous record of paleotemperature and other climatic proxies. Data from this core were recently used by Winograd and others (1997) to discuss the length and stability of the last four interglaciations. These data are given in table 1.
Ages were estimated by linear interpolation between age control points taken at key intervals in the core and analyzed by TIMS 230Th-234U-238U dating. The age estimates in Table 1 are based on the original 21 control points (see Table 2 in Ludwig, et al., 1992, and Figure 2 in Winograd, et al., 1992) as well as for the recently obtained TIMS age of 143.8±0.9 ka (2 sd analytical error) at 51.5 mm (Winograd, et al., 1997). The later sample was taken specifically for additional control in a critical portion of the core. Errors in the ages vary but are bounded by the errors in the appropriate control points. (See Table 2 in Ludwig, et al., 1992.)
They measured the age with radiometric decay products at 21 control points, and interpelated between them for samples where δ18O and δ13C were measured as indicators of climate. There is a table with the 284 samples by age with δ18O and δ13C values (the δ13C isotope is stable, unlike δ14C used for carbon dating).
quote:Devils Hole is a subaqueous cavern in south-central Nevada within a geographically detached unit of Death Valley National Park (fig. 1). The cavern is tectonic in origin and has developed in Cambrian carbonate rocks bordering the Ash Meadows oasis (Carr, 1988). The open fault zone comprising the cave extends to a depth of at least 130 meters below the water table, which is about 15 meters below land surface (Riggs and others, 1994). The primary source of groundwater flowing through Devils Hole, and discharging from the major springs within the oasis, is precipitation on the Spring Mountains to the east of the cavern ...
Since 1992, vein calcite samples have been uranium-series dated using thermal ionization mass spectrometric (TIMS) methodology (Ludwig and others, 1992). In 1997, the Devils Hole thorium-230 ages were independently confirmed by non-U.S. Geological Survey (USGS) investigators using protactinium-231 (Edwards and others, 1997).
Here we are interested in age versus depth within the calcite vein deposit. Here we have a series of data with three different pieces of information: calcite depth relative age, Thorium-230 content and Protactinium-231 content. The calcite relative age is corroborated by two independent radiometric methods.
So what exactly do we have here? Ground water (aquifer discharge) flowing slowly through a cave formed tectonically in carbonate rock, depositing calcite and various other minerals and impurities on the wall, including elements that are soluble in water, such as trace levels of radioactive isotopes of uranium.
These materials get deposited as the calcite forms, similar to the way sedimentary deposits trap organic deposits. The calcite builds up in a continous process, trapping the radioactive impurities and other material in their respective age related location. The calcite forms a solid rock matrix that holds these impurities in a position related to the time they were deposited in the calcite.
Radioactive elements decay into other elements, and some of these are not soluble, and thus the presence of these insoluble daughter elements is evidence of decay of the soluble parent elements. These daughter elements are still trapped in the layers of calcite that the parent elements were deposition in, so their position also relates to the age of the daughter elements in the calcite layers.
We are interested in two radioactive isotopes of these matrix constrained elements - thorium-230 and protactinium-231.
Using the half-lives of thorium-230 (75,380 years) and protactinium-231 (32,760 years), we can draw the exponential curves for these isotopes (with % on the y-axis and time in k-yrs on the x axis, thorium in blue and protactinium in red):
Like sedimentary layers, the law of superposition means that calcite depth is related to age, and this gives us a relative age system.
We also note that Thorium-230 has a half-life of 75,380 years, while Protactinium-231 has a half-life of 32,760 years - less than half the half-life of Thorium-230. This means that layer by layer the ratio of Thorium-230 to Protactinium-231 is different:
So for these dates to be invalid there would have to be a mechanism that can layer by layer preferentially change the ratio of these two (elements\isotopes) within the solid calcite vein, in what is now stone.
This also means that any fantasy about radioactive decay in the past being different than in the present, is invalid unless this changing ratio can be explained by a physical process, not fantasy.
quote:Two of the most frequently-used of these "uranium-series" systems are uranium-234 and thorium-230.
Like carbon-14, the shorter-lived uranium-series isotopes are constantly being replenished, in this case, by decaying uranium-238 supplied to the Earth during its original creation. Following the example of carbon-14, you may guess that one way to use these isotopes for dating is to remove them from their source of replenishment. This starts the dating clock. In carbon-14 this happens when a living thing (like a tree) dies and no longer takes in carbon-14 laden CO2. For the shorter-lived uranium-series radionuclides, there needs to be a physical removal from uranium. The chemistry of uranium and thorium are such that they are in fact easily removed from each other. Uranium tends to stay dissolved in water, but thorium is insoluble in water. So a number of applications of the thorium-230 method are based on this chemical partition between uranium and thorium.
On the other hand, calcium carbonates produced biologically (such as in corals, shells, teeth, and bones) take in small amounts of uranium, but essentially no thorium (because of its much lower concentrations in the water). This allows the dating of these materials by their lack of thorium. A brand-new coral reef will have essentially no thorium-230. As it ages, some of its uranium decays to thorium-230. While the thorium-230 itself is radioactive, this can be corrected for. The equations are more complex than for the simple systems described earlier, but the uranium-234 / thorium-230 method has been used to date corals now for several decades. Comparison of uranium-234 ages with ages obtained by counting annual growth bands of corals proves that the technique is highly accurate when properly used (Edwards et al., Earth Planet. Sci. Lett. 90, 371, 1988). The method has also been used to date stalactites and stalagmites from caves, already mentioned in connection with long-term calibration of the radiocarbon method. In fact, tens of thousands of uranium-series dates have been performed on cave formations around the world.
As with all dating, the agreement of two or more methods is highly recommended for confirmation of a measurement.
quote:Protactinium is a malleable, shiny, silver-gray radioactive metal that does not tarnish rapidly in air. It has a density greater than that of lead and occurs in nature in very low concentrations as a decay product of uranium. There are three naturally occurring isotopes, with protactinium-231 being the most abundant. ... The other two naturally occurring isotopes are protactinium-234 and protactinium-234m (the "m" meaning metastable), both of which have very short half-lives (6.7 hours and 1.2 minutes, respectively) and occur in extremely low concentrations.
Protactinium-231 is a decay product of uranium-235 and is present at sites that processed uranium ores and associated wastes. This isotope decays by emitting an alpha particle with a half-life of 33,000 years to actinium-227, which has a half-life of 22 years and decays by emitting an alpha or beta particle.
Protactinium is widely distributed in very small amounts in the earth's crust, and it is one of the rarest and most expensive naturally occurring elements. It is present in uranium ores at a concentration of about 1 part protactinium to 3 million parts uranium. Of the three naturally occurring isotopes, protactinium-231 is a decay product of uranium-235, and protactinium-234 and protactinium-234m are decay products of uranium-238.
The U-235 to Pa-231 decay is from a different series than the U-234 to Th-230 decay, so the two are independent of each other. Again, as the Devil's Hole calcite was deposited after being dissolved in water, the Pa-231 in the calcite could only come from the decay of the parent U-235, giving an accurate measurement of the age of the layers of calcite.
quote:A quantity is said to be subject to exponential decay if it decreases at a rate proportional to its value. Symbolically, this can be expressed as the following differential equation, where N is the quantity and λ is a positive number called the decay constant:
N(t) = N0e-λt
Here N(t) is the quantity at time t, and N0 = N(0) is the (initial) quantity, at time t=0.
If the decaying quantity is the number of discrete elements of a set, it is possible to compute the average length of time for which an element remains in the set. This is called the mean lifetime, and it can be shown that it relates to the decay rate,
T = 1/λ
The mean lifetime (also called the exponential time constant) is thus seen to be a simple "scaling time"
A more intuitive characteristic of exponential decay for many people is the time required for the decaying quantity to fall to one half of its initial value. This time is called the half-life, and often denoted by the symbol t1/2. The half-life can be written in terms of the decay constant, or the mean lifetime, as:
t1/2 = ln2/λ = Tln2
When this expression is inserted for T in the exponential equation above, and ln2 is absorbed into the base, this equation becomes:
A partial list of the parent and daughter isotopes and the decay half-lives is given in Table I. Notice the large range in the half-lives. Isotopes with long half-lives decay very slowly, and so are useful for dating correspondingly ancient events. Isotopes with shorter half-lives cannot date very ancient events because all of the atoms of the parent isotope would have already decayed away, like an hourglass left sitting with all the sand at the bottom. Isotopes with relatively short half-lives are useful for dating correspondingly shorter intervals, and can usually do so with greater accuracy, just as you would use a stopwatch rather than a grandfather clock to time a 100 meter dash. On the other hand, you would use a calendar, not a clock, to record time intervals of several weeks or more.
Table 1. Some Naturally Occurring Radioactive Isotopes and their half-lives
Radioactive Isotope (Parent)
The half-lives have all been measured directly either by using a radiation detector to count the number of atoms decaying in a given amount of time from a known amount of the parent material, or by measuring the ratio of daughter to parent atoms in a sample that originally consisted completely of parent atoms. Work on radiometric dating first started shortly after the turn of the 20th century, but progress was relatively slow before the late forties. However, by now we have had over fifty years to measure and re-measure the half-lives for many of the dating techniques. Very precise counting of the decay events or the daughter atoms can be done, so while the number of, say, rhenium-187 atoms decaying in 50 years is a very small fraction of the total, the resulting osmium-187 atoms can be very precisely counted. For example, recall that only one gram of material contains over 1021 (1 with 21 zeros behind) atoms. Even if only one trillionth of the atoms decay in one year, this is still millions of decays, each of which can be counted by a radiation detector!
The uncertainties on the half-lives given in the table are all very small. All of the half-lives are known to better than about two percent except for rhenium (5%), lutetium (3%), and beryllium (3%). There is no evidence of any of the half-lives changing over time. In fact, as discussed below, they have been observed to not change at all over hundreds of thousands of years.
There is another way to determine the age of the Earth. If we see an hourglass whose sand has run out, we know that it was turned over longer ago than the time interval it measures. Similarly, if we find that a radioactive parent was once abundant but has since run out, we know that it too was set longer ago than the time interval it measures. There are in fact many, many more parent isotopes than those listed in Table 1. However, most of them are no longer found naturally on Earth--they have run out. Their half-lives range down to times shorter than we can measure. Every single element has radioisotopes that no longer exist on Earth!
Now, if we look at which radioisotopes still exist and which do not, we find a very interesting fact. Nearly all isotopes with half-lives shorter than half a billion years are no longer in existence. For example, although most rocks contain significant amounts of Calcium, the isotope Calcium-41 (half-life 130,000 years does not exist just as potassium-38, -42, -43, etc. do not (Fig. 7). Just about the only radioisotopes found naturally are those with very long half-lives of close to a billion years or longer, as illustrated in the time line in Fig. 8.
The only isotopes present with shorter half-lives are those that have a source constantly replenishing them. Chlorine-36 (shown in Fig. 7) is one such "cosmogenic" isotope, ... In a number of cases there is evidence, particularly in meteorites, that shorter-lived isotopes existed at some point in the past, but have since become extinct. Some of these isotopes and their half-lives are given in Table II. This is conclusive evidence that the solar system was created longer ago than the span of these half lives! On the other hand, the existence in nature of parent isotopes with half lives around a billion years and longer is strong evidence that the Earth was created not longer ago than several billion years. The Earth is old enough that radioactive isotopes with half-lives less than half a billion years decayed away, but not so old that radioactive isotopes with longer half-lives are gone. This is just like finding hourglasses measuring a long time interval still going, while hourglasses measuring shorter intervals have run out.
The dense calcite formation in Devil's Hole is a closed system: once trapped by the deposition onto the formation the radioactive impurities are covered by layer after layer of newer deposits.
This means that radioactive impurities have nowhere to go, and thus they should be findable ... if they haven't decayed away.
We know that there were deposits of carbon in the calcite because they were measuring the δ13C content at each sample depth.
They were not measuring δ14C because it decays away after roughly 50,000 years, and once covered by calcite there is no way to replenish the 14C in the vein.
This is one of several cosmogenic isotopes that would be deposited in the formation.
This confirms that the calcite vein is older than 50,000 years, and this confirms that the earth is older that 50,000 years.